As a method of erasing a particular signal by employing an adaptive filter, the method in which a transversal type adaptive filter is employed is widely known. The adaptive filter, which is widely employed in an echo canceller, a noise canceller, a microphone array, or the like, generates a replica of the signal adaptively that is erased, and erases the signal by subtracting the replica from the signal.
Non-patent document 1 discloses the echo canceller as a technology of erasing an echo that leaks into a reception side from a transmission side in a four-line side of a two-line/four-line conversion circuit. The echo canceller operates in such a manner that it suppress the echo that leaks into the reception circuit side from the transmission circuit in the four-line side of the two-line/four-line conversion circuit by employing an adaptive FIR (Finite Impulse response) filter having a tap coefficient of which a numerical value is equal to or exceeds an impulse response length of an echo path and generates a pseudo echo (echo replica) corresponding to a transmitted signal. The acoustic echo canceller described in Non-patent document 2 is also known as a technology of erasing an acoustic echo, which is generated due to an acoustic coupling made between a loudspeaker for reproducing an acoustic signal and a microphone, with a similar technical principle.
In these echo cancellers, taking a scheme for correlating an error signal, which is obtained by subtracting the pseudo echo from a mixture in which the echo and the received signal are mixed, with a transmitted signal allows each tap coefficient of the adaptive filter to be modified. As a representative of such a coefficient modification algorithm of the adaptive filter, the LMS algorithm described in the Non-patent document 1 and the normalized LMS (least mean square) algorithm or a NLMS algorithm described in the Non-patent document 3 are widely known.    Patent document 1: JP-P1995-202765A    Non-patent document 1: Adaptive Signal Processing, 1985, Prentice-Hall Inc., USA    Non-patent document 2: Acoustic Echo Control (IEEE Signal Processing Magazine, PP. 42-69, July, 1999)    Non-patent document 3: Adaptive Filters, 1985, Kulwer Academic Publisher, USA    Non-patent document 4: Proceedings of European Signal Processing Conference, PP. 1182-1185, September, 1994    Non-patent document 5: Multirate Systems and Filter Banks, Prentice-Hall, 1993    Non-patent document 6: Adaptive Filters, Theory and Applications, John Wiley & Sons, 1998
Ideally, the error signal is equal to a difference between the echo and the echo replica (residual echo). However, realistically, the signals that disturb the update of the coefficient, for example, voice (near-end voice) that should be conveyed to a counterpart side, and a background noise exist. When these disturbing signals are smaller as compared with the residual echo, the disturbing signals can be neglected, and the filter coefficient can be correctly modified by employing the NLMS algorithm. However, when these disturbing signals become large, a problem that the filter coefficient cannot be modified correctly is raised.
In addition, when the input signal (reference input signal) of the adaptive filter is a non-stationary signal like the voice, as is the case may be, the filter coefficient cannot be correctly modified even though these disturbing signals are relatively small. This is due to the following reasons. At first, a reciprocal term of a reference input signal power is included in a step size for controlling a speed and a precision of the update of the filter coefficient, whereby the step size becomes very large when the reference input signal is very small. Further, the reason is that the echo is very small, correspondingly to the reference input signal, and the disturbing signal is relatively large as compared with the error signal. Thus, the filter coefficient results in being updated to a high level by employing not the error signal but the disturbing signal, and hence, the filter coefficient is not updated correctly.
The patent document 1 discloses the coefficient update algorithm that is capable of correctly updating the filter coefficient also in an environment in which the noise is large so as to cope with the problem that the filter coefficient cannot be correctly modified when the noise is large. The technology thereof is characterized in estimating the power of the reference input signal, and controlling the step size based upon a convex function such that a maximum value is gained when the foregoing reference input signal power coincides with a first threshold. Upon defining a coefficient vector, the error signal, a reference input signal vector at a discrete time (k) as w(k), e(k), and x(k), respectively, the coefficient update by the Patent document 1 can be expressed with the following equation.
                    [                  Numerical          ⁢                                          ⁢          equation          ⁢                                          ⁢          1                ]                                                                      w          ⁡                      (                          k              +              1                        )                          =                                            w              ⁡                              (                k                )                                      +                                                                                μ                    0                                    ⁢                                                            σ                      x                      2                                        ⁡                                          (                      k                      )                                                                                                                                  σ                      x                      4                                        ⁡                                          (                      k                      )                                                        +                                      α                    ⁢                                                                                  ⁢                                                                  σ                        n                        4                                            ⁡                                              (                        k                        )                                                                                                        ⁢                              e                ⁡                                  (                  k                  )                                            ⁢                              x                ⁡                                  (                  k                  )                                                              =                                    w              ⁡                              (                k                )                                      +                          Δ              ⁢                                                          ⁢                              w                ⁡                                  (                  k                  )                                                                                        (        1        )            
where σx2(x) is a reference input power, σn2(k) is an estimated noise power, μ0 and α are a constant, respectively. Further, Dw(k) is an updated quantity. σn2(k) can be obtained with the following equation.[Numerical equation 2]σn2(k+1)=βσn2(k)+(1−β)e2(k)  (2)
The noise estimated value is updated when the error signal is larger than the output of the adaptive filter.